There was a neat little fluke in baseball the other day. All fifteen of the Major League Baseball games on Tuesday were won by the home team. This appears to be the first time it’s happened since the league expanded to thirty teams in 1998. As best as the Elias Sports Bureau can work out, the last time every game was won by the home team was on the 23rd of May, 1914, when all four games in each of the National League, American League, and Federal League were home-team wins.
This produced talk about the home field advantage never having it so good, naturally. Also at least one article claimed the odds of fifteen home-team wins were one in 32,768. I can’t find that article now that I need it; please just trust me that it existed.
The thing is this claim is correct, if you assume there is no home-field advantage. That is, if you suppose the home team has exactly one chance in two of winning, then the chance of fifteen home teams winning is one-half raised to the fifteenth power. And that is one in 32,768.
This also assumes the games are independent, that is, that the outcome of one has no effect on the outcome of another. This seems likely, at least as long as we’re far enough away from the end of the season. In a pennant race a team might credibly relax once another game decided whether they had secured a position in the postseason. That might affect whether they win the game under way. Whether results are independent is always important for a probability question.
But stadium designers and the groundskeeping crew would not be doing their job if the home team had an equal chance of winning as the visiting team does. It’s been understood since the early days of organized professional baseball that the state of the field can offer advantages to the team that plays most of its games there.
Jack Jones, at Betfirm.com, estimated that for the five seasons from 2010 to 2014, the home team won about 53.7 percent of all games. Suppose we take this as accurate and representative of the home field advantage in general. Then the chance of fifteen home-team wins is 0.537 raised to the fifteenth power. That is approximately one divided by 11,230.
That’s a good bit more probable than the one in 32,768 you’d expect from the home team having exactly a 50 percent chance of winning. I think that’s a dramatic difference considering the home team wins a bit less than four percent more often than 50-50.
The follow-up question and one that’s good for a probability homework would be to work out what are the odds that we’d see one day with fifteen home-team wins in the mere eighteen years since it became possible.
nebusresearch 
Ok yet another strike for Joseph
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More of a soccer fan, eh? Well, I understand that.
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I shared this post on facebook with my son who loves baseball. He then wrote to me, “It’s also assuming not just that there is no homefield advantage, but that the two teams are evenly matched. In 10 of the 15 games, the team with the better overall record won. In only 9 of the games did the winning pitcher have a better ERA than the losing pitcher.”
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You’re right, it does assume the teams are equally matched. That’s not a justified assumption except as an admission of ignorance, that we might not know which team is better. (I assume that the full season is enough to indicate the strongest and the weakest teams, although it’s probably not enough to distinguish which is the 15th versus the 16th versus the 17th-strongest teams.)
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Sending this to my college pitcher and will be reading it with my 2 balls players at home today. Very cool, Joseph. Thank you!
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I hope he enjoyed, though I’d imagine he had seen some talk about the fluke already.
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My oldest son is our biggest baseball trivia geek, although we all enjoy cool stuff like this. There’s so much to keep up with so thanks for this one :D
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Oh, good. I’ve had the good fortune the past few years to read up on the history of baseball statistics — it grew up with the organization of baseball — and that’s fascinating stuff. Partly for the history, partly for the mathematics, partly for the sociology of trying to figure out what needs quantifying and how to do that.
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Exactly! When my oldest began playing baseball as a kid, I knew nothing about the sport. Nothing. So, I read everything I could get my hands on about it and fell in love, mainly through the history at first. Baseball is so rich!
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I have to admit I’m not much for playing baseball. I would have this problem of not sufficiently holding on to the bat after swinging, although the third baseman was able to jump out of the way of the bat every time. But the lore and the history and the evolution of the game are hard to resist. In short, I’ll buy pretty near anything Peter Morris writes.
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LOL! I’m with you about hitting a round ball with a round bat…how can anyone do that?! Morris’s “A Game of Inches” sounds terrific. Have you read it?
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It is a terrific book. I’ve read it and keep going back to leaf through it; there’s something fascinating on pretty near every page.
For example, you know how it’s legal for the runner to over-run first base? But not second or third? That’s the fossilized result of the decade or so when it was fashionable to play winter baseball on frozen ponds with all the players wearing ice skates.
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All right, then, it’s official. I need to read this book! Likely after Christmas, before spring training when I need a baseball fix :D
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Certainly, yes. It’ll fill that niche very nicely. It’s a thick book but everything in it is half- or one-page chunks, basically. And you can browse and graze rather than reading straight through.
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Perfect! Just added it to my Amazon wish list :D
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